Question 105555
{{{(625x^4y)^(1/4)/(16xy^3)^(3/4)}}}
Here are the useful exponent rules. 
{{{(xyz)^T=x^T*y^T*z^T}}}
{{{x^M*x^N=x^(M+N)}}}
{{{x^F/x^G=x^(F-G)}}}
{{{(x^P)^Q=x^(P*Q)}}}
Let's work on the numerator and denominator separately and then combine.
Numerator:
{{{(625x^4y)^(1/4)=625^(1/4)*x^(4*1/4)*y^(1/4)}}}Exponent rules from above. 
{{{(625x^4y)^(1/4)=5*x^(1)*y^(1/4)}}}Simplify.
{{{(625x^4y)^(1/4)=5xy^(1/4)}}}
Denominator:
{{{(16xy^3)^(3/4)=16^(3/4)*x^(3/4)*y^(3*3/4)}}}Exponent rules from above.
{{{(16xy^3)^(3/4)=8x^(3/4)*y^(9/4)}}}Simplfy.
Now let's combine them back together:
{{{(625x^4y)^(1/4)/(16xy^3)^(3/4)=5xy^(1/4)/(8x^(3/4)*y^(9/4))}}}
{{{(625x^4y)^(1/4)/(16xy^3)^(3/4)=5x^(1-3/4)y^(1/4-9/4)/(8)}}}Exponent rules from above.
{{{(625x^4y)^(1/4)/(16xy^3)^(3/4)=5x^(1/4)y^(-2)/(8)}}}Simplify.
{{{(625x^4y)^(1/4)/(16xy^3)^(3/4)=5x^(1/4)/(8y^2)}}}Final answer.